published_or_final_version / Economics and Finance / Master / Master of Economics

The problem was to determine the levels of intellectual capacity necessary at various ages for acquiring rapid and efficient nonspatial discrimination learning sets on problems of increasing complexity.

The problem undertaken in this paper is to determine what the algebraic structure of the class of C-sets is, when the notion of sum is to be the "set sum. " While the preliminary work done by Appling took place in the space of additive and bounded real valued functions, the results here are found in the more general setting of a complete lattice ordered group. As a conseque n c e , G . Birkhof f' s book, Lattice Theory, is used as the standard reference for most of the terminology used in the paper. The direction taken is prompted by a paper by W. D. L. Appling, "A Generalization of Absolute Continuity and of an Analogue of the Lebesgue Decomposition Theorem. " Since some of the results obtained provide another approach to a problem originally studied by Nakano, and improved upon by Bernau, reference is made to their work to provide other terminology and examples of alternative approaches to the problem of lateral completion. Thus Chapter I contains a brief history of the notion of C-sets and their relationship to lattice ordered groups, along with a summary of the properties of lattice ordered groups needed for later developments. In addition, several results in the general theory of lattice ordered groups are cited to provide insight into the comparability of the assumptions that will ultimately be made about the groups. Chapter II begins with the axiomatization of the collection of nearest point functions" for the closed A-ideals of the cone of a complete lattice ordered group. The basic results in the chapter establish that the functions defined do indeed characterize the complete A-ideals, and that the maps have a 'nearest point property." The maps are then extended to the entire group and shown to correspond to the "nearest point maps" for a C-set in PAB' Chapter III is devoted to exploring the algebraic structures found in the collection of all closed A-ideal maps, denoted J. J is shown to be a lattice ordered monoid, abelian and complete, containing a maximal group cone P*. It is further shown that the original group cone P is isomorphic to a subset of P*. Chapter IV looks into a rather interesting characterization of P*, one that, in the terminology of Bernau, implies that P* is the cone of the group that is the lateral completion of the original group. A final result is a demonstration that the members of j each have a representation as the sum of an element of P* and an additive element of j.

In this paper we present a fuzzy voting scheme for cluster algorithms. This fuzzy voting method allows us to combine several runs of cluster algorithms resulting in a common fuzzy partition. This helps us to overcome instabilities of the cluster algorithms and results in a better clustering. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Probability theory is a branch of mathematics concerned with determining the long run frequency or chance that a given event will occur. This chance is determined by dividing the number of selected events by the number of total events possible, assuming these events are equally likely. Probability theory is simply enumerative combinatorial analysis when applied to finite sets. For a given finite sample space, probability questions are usually "just" a lot of counting. The purpose of this thesis is to provide some in depth analysis of several combinatorial methods, including basic principles of counting, permutations and combinations, by specifically exploring one type of probability problem: C ordered possible elements that are equally likely s independent sampled subjects r distinct elements, where r = 1, 2, 3, …, min (C, s) we want to know P(s subjects utilize exactly r distinct elements). This thesis gives a detailed step by step analysis on techniques used to ultimately finding a general formula to solve the above problem.

Call number: LD2668 .T4 1986 H53 / Master of Science / Electrical and Computer Engineering

The axial map of a town is one of the key components of the space syntax method – a tool for analysing urban layout. It is derived by placing the longest and fewest lines, called axial lines, to cross the adjacencies between convex polygons in a convex map of a town. Previous research has shown that placing axial lines to cross the adjacencies between a collection of convex polygons is NP-complete, even when the convex polygons are restricted to rectangles and the axial lines to have orthogonal orientation. In this document, we show that placing orthogonal axial lines in orthogonal rectangles where the adjacencies between the rectangles are restricted to be crossed only once (ALPSC- OLOR) is NP-complete. As a result, we infer the single adjacency crossing version of the general axial line placement problem is NP-complete. The transformation of NPcompleteness of ALP-SC-OLOR is from vertex cover for biconnected planar graphs. A heuristic is then presented that gives a reasonable approximate solution to ALP-SC-OLOR based on a greedy method.

To find out what differs between two versions of a file can be done with several different techniques and programs. These techniques and programs are often focusd on finding differences in text files, in documents, or in class files for programming. An example of a program is the popular git tool which focuses on displaying the difference between versions of files in a project. A common way to find these differences is to utilize an algorithm called Longest common subsequence, which focuses on finding the longest common subsequence in each file to find similarity between the files. By excluding all similarities in a file, all remaining text will be the differences between the files. The Longest Common Subsequence is often used to find the differences in an acceptable time. When two lines in a file is compared to see if they differ from each other hashing is used. The hash values for each correspondent line in both files will be compared. Hashing a line will give the content on that line a unique value. If as little as one character on a line is different between the version, the hash values for those lines will be different as well. These techniques are very useful when comparing two versions of a file with text content. With data from a database some, but not all, of these techniques can be useful. A big difference between data in a database and text in a file will be that content is not just added and delete but also updated. This thesis studies the problem on how to make use of these techniques when finding differences between large datasets, and doing this in a reasonable time, instead of finding differences in documents and files.  Three different methods are going to be studied in theory. These results will be provided in both time and space complexities. Finally, a selected one of these methods is further studied with implementation and testing. The reason only one of these three is implemented is because of time constraint. The one that got chosen had easy maintainability, an easy implementation, and maintains a good execution time.

We consider closed orientable surfaces S of genus greater than one and homeomorphisms f homotopic to the identity. A set of hypotheses is presented, called fully essential system of curves, and it is shown that under these hypotheses, the natural lift of f to the universal cover of S (the Poincaré disk), has complicated and rich dynamics. We also show that the homological rotation set of such a f is a compact convex set with maximal dimension and all points in its interior are realized by compact f-invariant sets, periodic orbits in the rational case. / Consideramos superfícies fechadas orientáveis S de gênero maior do que um e homeomorfismos f homotópicos a identidade. Apresentamos um conjunto de hipóteses, chamado sistema de curvas totalmente essencial, e mostramos que sob essas hipóteses, o levantamento natural de f para o recobrimento universal de S (o disco de Poincaré), tem uma dinâmica rica e complicada. Mostramos também que o conjunto de rotação homológico de f é um subconjunto compacto convexo de dimensão máxima e todos os pontos no seu interior são realizados por conjuntos compactos f-invariantes, órbitas periódicas no caso racional.

by Lo I Fan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references. / Chapter Chapter 1: --- Introduction / Chapter 1.1 --- The Evolution of Fonts --- p.1 / Chapter 1.2 --- Bitmap Fonts --- p.2 / Chapter 1.3 --- Outline Fonts / Chapter 1.3.1 --- Arc and Vector Form --- p.4 / Chapter 1.3.2 --- Spline Form --- p.4 / Chapter 1.3.3 --- Pros and Cons of Outline Fonts --- p.8 / Chapter 1.4 --- Examples of Outline Fonts / Chapter 1.4.1 --- Adobe's PostScript --- p.9 / Chapter 1.4.2 --- Apple's and Microsoft TrueType / Chapter 1.4.2.1 --- Outline Representation --- p.10 / Chapter 1.4.2.2 --- Rasterisation --- p.12 / Chapter 1.4.2.3 --- Hinting --- p.13 / Chapter 1.5 --- Bold Fonts / Chapter 1.5.1 --- Definition of Bold --- p.15 / Chapter 1.5.2 --- Definition of Auto B oldness --- p.16 / Chapter 1.5.3 --- Auto Boldness by Double Printing --- p.17 / Chapter 1.5.4 --- Auto Boldness by Multi-Master Technique --- p.18 / Chapter 1.6 --- Chinese Fonts / Chapter 1.6.1 --- Chinese Character Sets --- p.19 / Chapter 1.6.2 --- The Subtleties of Chinese Fonts Auto Boldness --- p.21 / Chapter 1.7 --- Project Objective --- p.23 / Chapter 1.8 --- Goals --- p.23 / Chapter Chapter 2: --- Main Ideas of Chinese Font Auto Boldness / Chapter 2.1 --- Prototype of Auto Boldness Driver --- p.24 / Chapter 2.2 --- Design Features of the Prototype Auto Boldness Driver --- p.25 / Chapter 2.3 --- Data Structure and Algorithm of Auto Boldness / Chapter 2.3.1 --- Data Structure of TrueType Character Outline --- p.27 / Chapter 2.3.2 --- Algorithm of Auto Boldness --- p.28 / Chapter 2.3.3 --- Algorithm Description --- p.29 / Chapter 2.4 --- Component Font Auto Boldness --- p.35 / Chapter Chapter 3: --- Language of Auto Boldness / Chapter 3.1 --- Enhancements of TrueType Engine to support Auto Boldness --- p.36 / Chapter 3.2 --- Symmetric Bold Instruction --- p.38 / Chapter 3.3 --- Rotate Bold Instruction --- p.47 / Chapter 3.4 --- Asymmetric B old Instruction --- p.50 / Chapter 3.5 --- Comparison of Bold Instructions --- p.54 / Chapter 3.6 --- Serif Accommodation Instruction --- p.55 / Chapter Chapter 4: --- Shape Parsing and Auto Bold Code Generation / Chapter 4.1 --- Compilation Process and Auto Boldness --- p.62 / Chapter 4.2 --- Shape Lexical Analyzer --- p.64 / Chapter 4.3 --- Shape Token Attributes Evaluation / Chapter 4.3.1 --- line Token --- p.66 / Chapter 4.3.2 --- bezier2 Token --- p.67 / Chapter 4.3.3 --- sharp Token --- p.70 / Chapter 4.3.4 --- concave Token --- p.75 / Chapter 4.3.5 --- convex Token --- p.75 / Chapter 4.4 --- Scope of Shape Parsing --- p.76 / Chapter 4.5 --- Shape Parsing Mechanism --- p.77 / Chapter 4.6 --- Model Grammar Rules / Chapter 4.6.1 --- Grammar Rule Format --- p.81 / Chapter 4.6.2 --- Grammar Rule Item --- p.82 / Chapter 4.6.3 --- Grammar Rule Assignment --- p.83 / Chapter 4.6.4 --- Grammar Rule Condition --- p.83 / Chapter 4.7 --- Auto Boldness Code Generation --- p.84 / Chapter 4.8 --- Program Methodology of Prototype Auto Boldness Driver --- p.86 / Chapter Chapter 5: --- Conclusions / Chapter 5.1 --- Work Achieved --- p.87 / Chapter 5.2 --- The Pros and Cons of Auto Boldness Algorithm --- p.88 / Chapter 5.3 --- Bold Quality Assessments --- p.91 / Chapter 5.3 --- Future Directions --- p.93 / References / Appendix One / Appendix Two